Declare a global variable in a Blender session
If you want data to be global in Python, (within a Blender session).

Typically its best to create a module with a unique name specific to your project, import it - and access variables in that module.

Every script which imports the module will be viewing the same data.

In this exact case it sounds like you should add the object it self to a module.

import my_module
my_module.my_obj = obj




Some other script

import my_module
obj = my_module.my_obj